Simplify the following expression: $ n = \dfrac{6k}{-8k - 4} - \dfrac{-4}{5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{6k}{-8k - 4} \times \dfrac{5}{5} = \dfrac{30k}{-40k - 20} $ Multiply the second expression by $\dfrac{-8k - 4}{-8k - 4}$ $ \dfrac{-4}{5} \times \dfrac{-8k - 4}{-8k - 4} = \dfrac{32k + 16}{-40k - 20} $ Therefore $ n = \dfrac{30k}{-40k - 20} - \dfrac{32k + 16}{-40k - 20} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{30k - (32k + 16) }{-40k - 20} $ Distribute the negative sign: $n = \dfrac{30k - 32k - 16}{-40k - 20}$ $n = \dfrac{-2k - 16}{-40k - 20}$ Simplify the expression by dividing the numerator and denominator by -2: $n = \dfrac{k + 8}{20k + 10}$